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Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models
Author(s) -
Pan Qiyun,
Byon Eunshin,
Ko Young Myoung,
Lam Henry
Publication year - 2020
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21938
Subject(s) - quantile , variance reduction , importance sampling , sampling (signal processing) , computer science , adaptive sampling , monte carlo method , variance (accounting) , mathematical optimization , reliability (semiconductor) , extreme value theory , black box , convergence (economics) , reduction (mathematics) , algorithm , statistics , mathematics , artificial intelligence , power (physics) , physics , geometry , accounting , filter (signal processing) , quantum mechanics , economics , business , computer vision , economic growth
Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.